Building upon our recent studies devoted to the bonding changes in polar reactions [RSC Advances, 2012, 2, 1334 and Org. Biomol. Chem., 2012, 10, 3841], we propose herein two new electrophilic, P⁺ _k, and nucleophilic, P⁻ _k, Parr functions based on the spin density distribution at the radical anion and at the radical cation of a neutral molecule. These local functions allow for the characterisation of the most electrophilic and nucleophilic centres of molecules, and for the establishment of the regio- and chemoselectivity in polar reactions. The proposed Parr functions are compared with both, the Parr–Yang Fukui functions [J. Am. Chem. Soc. 1984, 106, 4049] based on frontier molecular orbitals, and Yang–Mortier condensed Fukui functions [J. Am. Chem. Soc. 1986, 108, 5708] based on Mulliken charges.

A good correlation between the activation energy and the polar character of Diels–Alder reactions measured as the charge transfer at the transition state structure has been found. This electronic parameter controls the reaction rate to an even greater extent than other recognized structural features. The proposed polar mechanism, which is characterized by the electrophilic/nucleophilic interactions at the transition state structure, can be easily predicted by analyzing the electrophilicity/nucleophilicity indices defined within the conceptual density functional theory. Due to the significance of the polarity of the reaction, Diels–Alder reactions should be classified as non-polar (N), polar (P), and ionic (I).

The molecular mechanism of the Povarov reaction in acetonitrile has been studied at the MPWB1K/6-311G** level of theory. This reaction follows a domino process that comprises two sequential reactions: (i) a Lewis acid catalysed aza-Diels–Alder (A-DA) reaction between a N-aryl imine and a nucleophilic ethylene yielding a formal [4 + 2] cycloadduct; (ii) a stepwise 1,3-hydrogen shift at this intermediate affording the final tetrahydroquinoline. At this computational level, the Lewis acid catalysed A-DA reaction presents a two-step mechanism as a consequence of the large stabilisation of the corresponding zwitterionic intermediate. Our study allows establishing that the N-aryl substituent has no remarkable incidence in the activation energy, but the presence of a second C-aryl substituent has a relevant role in the reaction rate. Analysis of the DFT-based reactivity indices of the reagents provides further explanation of the behaviours of the mechanism of the A-DA reaction involved in the Povarov reaction.